why is everything to the power of 0 1?
In: 3
The true reason is that humans invented math and they decided that’s how they wanted it to work!
But let me explain why they chose that by showing a pattern.
3^3 = 27
3^2 = 9
3^1 = 3
As we subtract 1 from the exponent, we divide the result by 3.
So what’s should 3^0 be? If we follow the pattern, 3^0 should be 1.
Another way to look at this is by thinking about mathematical “identities.” An identity in math is a special number that leaves anything it touches unchanged. When adding or subtracting, the identity is 0. If you add 0 or subtract 0, you don’t change anything. But for multiplying and dividing, the identity is 1.
Remember earlier we said that when we subtract from the exponent, we divide from the final result? Well now it makes sense. When we have the subtracting identity in the exponent, we should have the dividing identity in the final result. That’s why anything to the 0 power becomes 1. Although I should point out these are normally called the additive identity and multiplicative identity, even though they work for subtracting and dividing too.
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